Consistency of Chi-Squared Test with Varying Number of Classes  

作　　者：HUANG Rui CUI Hengjian 

机构地区：[1]College of Mathematic and Statistics,Jishou University [2]School of Mathematical Sciences,Beijing Normal University [3]Department of Statistics,School of Mathematical Sciences,Capital Normal University

出　　处：《Journal of Systems Science & Complexity》2015年第2期439-450,共12页系统科学与复杂性学报（英文版）

基　　金：supported by the Natural Science Foundation of China under Grant Nos.11071022,11028103,11231010,11471223,BCMIIS;the Beijing Municipal Educational Commission Foundation under Grant Nos.KZ201410028030,KM201210028005;Jishou University Subject in 2014(No:14JD035)

摘　　要：The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.

关 键 词：Consistency of chi-squared test goodness of fit test varying number of classes. 

分 类 号：O212.1[理学—概率论与数理统计] O121.4[理学—数学]